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Question 446

In aerodynamic testing, the drag coefficient CDC_DCD​ of a specialized wing profile is modeled using the following definite integral related to the airflow pressure distribution:

CD=∫2312(4−w2)32 dw C_D = \int_{\sqrt{2}}^{\sqrt{3}} \frac{12}{(4 - w^2)^{\frac{3}{2}}} \, dw CD​=∫2​3​​(4−w2)23​12​dw

By using the substitution w=2sin⁡θw = 2 \sin \thetaw=2sinθ, determine the exact value of CDC_DCD​.

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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